Find the coordinates of the vertices of a triangle, the equations of whose sides are : y(t 1 + t 2 ) = 2x + 2at 1 t 2 . y(t 2 + t 3 ) = 2x + 2at 2 t 3 and, y(t 3 + t 1 ) = 2x + 2at 1 t 3 .

Question

Philoid · Accepted Answer

Given:

y (t₁ + t₂) = 2x + 2a t₁t₂, y (t₂ + t₃) = 2x + 2a t₂t₃ and y (t₃ + t₁) = 2x + 2a t₁t₃

To find:

Point of intersection of pair of lines.

Concept Used:

Point of intersection of two lines.

Explanation:

2x − y (t₁ + t₂) + 2a t₁t₂ = 0 … (1)

2x − y (t₂ + t₃) + 2a t₂t₃ = 0 … (2)

2x − y (t₃ + t₁) + 2a t₁t₃ = 0 … (3)

Solving (1) and (2) using cross - multiplication method:

Solving (1) and (3) using cross - multiplication method:

Solving (2) and (3) using cross - multiplication method:

Hence, the coordinates of the vertices of the triangle are

Find the coordinates of the vertices of a triangle, the equations of whose sides are :y(t1 + t2) = 2x + 2at1t2. y(t2 + t3) = 2x + 2at2t3 and, y(t3 + t1) = 2x + 2at1t3.

Find the coordinates of the vertices of a triangle, the equations of whose sides are :
y(t₁ + t₂) = 2x + 2at₁t₂. y(t₂ + t₃) = 2x + 2at₂t₃ and, y(t₃ + t₁) = 2x + 2at₁t₃.